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An airplane is flying at a velocity of 321.71 m/s in a direction 32 degrees north of west. What are the magnitudes and directions of the components of this velocity vector? (2 points)
301.1 m/s to the west, 96.38 m/s to the south
272.8 m/s to the west, 170.5 m/s to the north
102.5 m/s to the west, 264.4 m/s to the north
201.7 m/s to the east, 98.1 m/s to the north

Respuesta :

In triangle ABC

AB = V = velocity of the airplane = 321.71 m/s

BC = [tex]V_{ox}[/tex] = horizontal component of the velocity of airplane

AC = [tex]V_{oy}[/tex] = vertical component of the velocity of airplane

using the trigonometric formula

Cos32 = BC/AB

Cos32 = [tex]V_{ox}[/tex] /321.71

[tex]V_{ox}[/tex] = (321.71) Cos32

[tex]V_{ox}[/tex] = 272.83 m/s

direction : towards west


using the trigonometric formula

Sin32 = AC/AB

Sin32 = [tex]V_{oy}[/tex] /321.71

[tex]V_{ox}[/tex] = (321.71) Sin32

[tex]V_{ox}[/tex] = 170.5 m/s

direction : towards north


272.8 m/s to the west, 170.5 m/s to the north

Ver imagen JemdetNasr

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